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Question Number 106653 by Dwaipayan Shikari last updated on 06/Aug/20

$$30+144+420+960+1890+3360+...n$$

Commented by Dwaipayan Shikari last updated on 06/Aug/20

$$y_0△y_0{△}^2{y}_0{△}^3{y}_0{△}^4{y}_0$$$$30$$$$114$$$$144162$$$$276102$$$$42026424$$$$540126$$$$96039024$$$$930150$$$$1890540$$$$1470$$$$3360$$$$\varphi \left(y_0\right)=y_0+(n-1)△y_0+(n-1)(n-2)\frac{{△}^2{y}_0}{2!}+(n-1)(n-2)(n-3)\frac{{△}^3{y}_0}{3!}$$$$+(n-1)(n-2)(n-3)(n-4)\frac{{△}^4{y}_0}{4!}$$$$\varphi \left(y_0\right)=30+(n-1)(114+81n-62+102+8n^2-85n+n^3+6n+20n-24)$$$$\varphi \left(y_0\right)=30+(n-1)(n^3+8n^2+22n+30)=n^4+14n^2+7n^3+8n$$$$\underset{n=1}{\sum ^n}\varphi \left(y_0\right)=\underset{n=1}{\sum ^n}{n}^4+14n^2+7n^3+8n=\frac{1}{20}n(n+1)(n+2)(n+3)(4n+21)$$

Commented by Ar Brandon last updated on 06/Aug/20

�� What's this ?

Commented by Dwaipayan Shikari last updated on 06/Aug/20

$${Newton}^{\prime }sinterpolationformula$$

Commented by Ar Brandon last updated on 06/Aug/20

OK��

Commented by Dwaipayan Shikari last updated on 06/Aug/20

https://en.wikipedia.org/wiki/Newton_polynomial

Commented by Dwaipayan Shikari last updated on 06/Aug/20

https://en.wikipedia.org/wiki/Interpolation

Commented by Ar Brandon last updated on 06/Aug/20

Thanks

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